Fluid dynamics of floated floors

Abstract

In the design of a floated floor, it is important that no acoustic spring be set up in the air cavity between the floor and the supporting slab. An ingeneous heuristic analysis of this problem has been given [E.E. Ungar, Noise Control Eng. 5(1), 12–16 (Jul.–Aug. 1975)]. To rigorously define the acoustic problem of the response of a small cavity to a moving wall, first-order perturbations of the Navier-Stokes equations have been written, wherein viscous and thermal effects are included, in addition to the usual acoustic (potential flow) terms. The inclusion of viscous terms allows the satisfaction of tangential and normal velocity boundary conditions, thus accounting for the possibility of large lateral flow velocities when the cavity is vented at the lateral edges. When viscous and thermal effects are of comparable magnitude, the governing equations uncouple into a damped wave equation and a diffusion equation. The solution, for time-harmonic dependence, allows the prediction of the relative cavity geometry, i.e., size and venting of the cavity, in order to avoid generation of an acoustic spring.